There are also these:
הוא שאל לעצתו
הוא שאל לרצונו
And I think you can say many other things using this construction.
I can't seem to come up with a definite English translation, but it's something between "He asked to know about...", and "He asked (ביקש) him for...".

In general, "ask [enquire] sbdy" = ... לשאול את and "answer sbdy" = לענות ל..
לשאול ל... is used in some cases, but not with pronouns. It has a similar meaning to "enquired as for ..."/"enquired for ..."

Right:ענה על מכתב. Also ענה על השאלה (as was indicated in a previous post), ענה על מייל, ענה על מאמר, ענה על הטענותת, etc. Also ענה על הציפיות (met the expectations), which is an idiom.
But I fear we have strayed from the original שאל to ענה .